When I first saw this thread I wondered if Molly was related to Peggy - because I just finished doing a midi of Peggy. (Which is here if you're interested). The words to this don't have anything to do with swans so I didn't correlate the two. According to Bruce's site Peggy Bawn:

appears in The Scots Musical Museum (1787 - 1802). The song, without music appears in a companion to the Scots Musical Museum dated around 1772.

Is Lord Kenneth and Fair Ellinour supposed to be a variant of Lord Thomas and Fair Ellinor? Both melodically and lyrically the Peggy Bawn I found seem to be far from that - but, of course, that's why I enjoy traditional music!